def test_saveloadtxt(self):
tmp_file = NamedTemporaryFile(mode='wb', delete=False)
tmp_file.close()
x = 3.14159265359
tools.savetxt(tmp_file.name, x)
self.assertAlmostEqual(x, tools.loadtxt(tmp_file.name), 6)
def compute_direction(cls):
""" Computes model update direction from stored function and gradient
values
"""
unix.cd(cls.path)
m_new = loadnpy('m_new')
f_new = loadtxt('f_new')
g_new = loadnpy('g_new')
if PAR.SCHEME == 'GradientDescent':
p_new = -g_new
elif PAR.SCHEME == 'ConjugateGradient':
# compute NLCG udpate
p_new = cls.NLCG.compute()
elif PAR.SCHEME == 'QuasiNewton':
# compute L-BFGS update
if cls.iter == 1:
p_new = -g_new
else:
cls.LBFGS.update()
p_new = -cls.LBFGS.solve()
# save results
unix.cd(cls.path)
savenpy('p_new', p_new)
savetxt('s_new', np.dot(g_new, p_new))
def finalize_search(cls):
""" Cleans working directory and writes updated model
"""
unix.cd(cls.path)
m0 = loadnpy('m_new')
p = loadnpy('p_new')
x = cls.step_lens()
f = cls.func_vals()
# clean working directory
unix.rm('alpha')
unix.rm('m_try')
unix.rm('f_try')
if cls.iter > 1:
unix.rm('m_old')
unix.rm('f_old')
unix.rm('g_old')
unix.rm('p_old')
unix.rm('s_old')
unix.mv('m_new', 'm_old')
unix.mv('f_new', 'f_old')
unix.mv('g_new', 'g_old')
unix.mv('p_new', 'p_old')
unix.mv('s_new', 's_old')
# write updated model
alpha = x[f.argmin()]
savetxt('alpha', alpha)
savenpy('m_new', m0 + p * alpha)
savetxt('f_new', f.min())
cls.writer([], [], [])
def compute_step(cls):
""" Computes next trial step length
"""
unix.cd(cls.path)
m0 = loadnpy('m_new')
p = loadnpy('p_new')
f0 = loadtxt('f_new')
g0 = loadtxt('s_new')
x = cls.step_lens()
f = cls.func_vals()
# compute trial step length
if PAR.SRCHTYPE == 'Backtrack':
alpha = lib.backtrack2(f0, g0, x[1], f[1], b1=0.1, b2=0.5)
elif PAR.SRCHTYPE == 'Bracket':
FACTOR = 2.
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = lib.polyfit2(x, f)
elif any(f[1:] < f[0]):
alpha = loadtxt('alpha') * FACTOR
else:
alpha = loadtxt('alpha') * FACTOR**-1
elif PAR.SRCHTYPE == 'Fixed':
alpha = cls.step_ratio * (step + 1) * PAR.STEPLEN
else:
raise ValueError
# write trial model
savetxt('alpha', alpha)
savenpy('m_try', m0 + p * alpha)
def test_savetxt(self):
filename = "tmp_savetxt"
x = 3.14159265359
tools.savetxt(filename, x)
with open(filename, 'r') as f:
y = float(f.readline())
os.remove(filename)
self.assertAlmostEqual(x, y, places=6)
def initialize_search(cls):
""" Determines initial step length for line search
"""
unix.cd(cls.path)
if cls.iter == 1:
s_new = loadtxt('s_new')
f_new = loadtxt('f_new')
else:
s_old = loadtxt('s_old')
s_new = loadtxt('s_new')
f_old = loadtxt('f_old')
f_new = loadtxt('f_new')
alpha = loadtxt('alpha')
m = loadnpy('m_new')
p = loadnpy('p_new')
# reset search history
cls.search_history = [[0., f_new]]
cls.isdone = 0
cls.isbest = 0
cls.isbrak = 0
# determine initial step length
len_m = max(abs(m))
len_d = max(abs(p))
cls.step_ratio = float(len_m / len_d)
if cls.iter == 1:
assert PAR.STEPLEN != 0.
alpha = PAR.STEPLEN * cls.step_ratio
elif PAR.SRCHTYPE in ['Bracket']:
alpha *= 2. * s_old / s_new
elif PAR.SCHEME in ['GradientDescent', 'ConjugateGradient']:
alpha *= 2. * s_old / s_new
else:
alpha = 1.
# ad hoc scaling
if PAR.ADHOCSCALING:
alpha *= PAR.ADHOCSCALING
# limit maximum step length
if PAR.STEPMAX > 0.:
if alpha / cls.step_ratio > PAR.STEPMAX:
alpha = PAR.STEPMAX * cls.step_ratio
# write trial model
savenpy('m_try', m + p * alpha)
savetxt('alpha', alpha)
cls.writer(cls.iter, 0., f_new)
def finalize_search(self):
""" Cleans working directory and writes updated model
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
x = self.step_lens()
f = self.func_vals()
# clean working directory
unix.rm('alpha')
unix.rm('m_try')
unix.rm('f_try')
if self.iter > 1:
unix.rm('m_old')
unix.rm('f_old')
unix.rm('g_old')
unix.rm('p_old')
unix.rm('s_old')
unix.mv('m_new', 'm_old')
unix.mv('f_new', 'f_old')
unix.mv('g_new', 'g_old')
unix.mv('p_new', 'p_old')
unix.mv('s_new', 's_old')
# write updated model
alpha = x[f.argmin()]
savetxt('alpha', alpha)
self.save('m_new', m + alpha * p)
savetxt('f_new', f.min())
# append latest statistics
self.writer('factor',
-self.dot(g, g)**-0.5 * (f[1] - f[0]) / (x[1] - x[0]))
self.writer('gradient_norm_L1', np.linalg.norm(g, 1))
self.writer('gradient_norm_L2', np.linalg.norm(g, 2))
self.writer('misfit', f[0])
self.writer('restarted', self.restarted)
self.writer('slope', (f[1] - f[0]) / (x[1] - x[0]))
self.writer('step_count', self.step_count)
self.writer('step_length', x[f.argmin()])
self.writer('theta', 180. * np.pi**-1 * angle(p, -g))
self.stepwriter.newline()
def finalize_search(self):
""" Cleans working directory and writes updated model
"""
unix.cd(PATH.OPTIMIZE)
m = self.load("m_new")
g = self.load("g_new")
p = self.load("p_new")
s = loadtxt("s_new")
x = self.step_lens()
f = self.func_vals()
# clean working directory
unix.rm("alpha")
unix.rm("m_try")
unix.rm("f_try")
if self.iter > 1:
unix.rm("m_old")
unix.rm("f_old")
unix.rm("g_old")
unix.rm("p_old")
unix.rm("s_old")
unix.mv("m_new", "m_old")
unix.mv("f_new", "f_old")
unix.mv("g_new", "g_old")
unix.mv("p_new", "p_old")
unix.mv("s_new", "s_old")
# write updated model
alpha = x[f.argmin()]
savetxt("alpha", alpha)
self.save("m_new", m + alpha * p)
savetxt("f_new", f.min())
# append latest output
self.writer("factor", -self.dot(g, g) ** -0.5 * (f[1] - f[0]) / (x[1] - x[0]))
self.writer("gradient_norm_L1", np.linalg.norm(g, 1))
self.writer("gradient_norm_L2", np.linalg.norm(g, 2))
self.writer("misfit", f[0])
self.writer("restarted", self.restarted)
self.writer("slope", (f[1] - f[0]) / (x[1] - x[0]))
self.writer("step_count", self.step_count)
self.writer("step_length", x[f.argmin()])
self.writer("theta", 180.0 * np.pi ** -1 * angle(p, -g))
self.stepwriter.newline()
def finalize_search(self):
""" Cleans working directory and writes updated model
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
x = self.step_lens()
f = self.func_vals()
# clean working directory
unix.rm('alpha')
unix.rm('m_try')
unix.rm('f_try')
if self.iter > 1:
unix.rm('m_old')
unix.rm('f_old')
unix.rm('g_old')
unix.rm('p_old')
unix.rm('s_old')
unix.mv('m_new', 'm_old')
unix.mv('f_new', 'f_old')
unix.mv('g_new', 'g_old')
unix.mv('p_new', 'p_old')
unix.mv('s_new', 's_old')
# write updated model
alpha = x[f.argmin()]
savetxt('alpha', alpha)
self.save('m_new', m + alpha*p)
savetxt('f_new', f.min())
# append latest statistics
self.writer('factor', -self.dot(g,g)**-0.5 * (f[1]-f[0])/(x[1]-x[0]))
self.writer('gradient_norm_L1', np.linalg.norm(g, 1))
self.writer('gradient_norm_L2', np.linalg.norm(g, 2))
self.writer('misfit', f[0])
self.writer('restarted', self.restarted)
self.writer('slope', (f[1]-f[0])/(x[1]-x[0]))
self.writer('step_count', self.step_count)
self.writer('step_length', x[f.argmin()])
self.writer('theta', 180.*np.pi**-1*angle(p,-g))
self.stepwriter.newline()
def initialize(self):
unix.mkdir(self.path+'/'+'LCG')
unix.cd(self.path)
self.iter += 1
self.ilcg = 0
r = self.load('g_new')
x = np.zeros(r.size)
self.save('LCG/x', x)
self.save('LCG/r', r)
y = self.apply_precond(r)
p = -y
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
def initialize(self):
unix.mkdir(self.path + '/' + 'LCG')
unix.cd(self.path)
self.iter += 1
self.ilcg = 0
r = self.load('g_new')
x = np.zeros(r.size)
self.save('LCG/x', x)
self.save('LCG/r', r)
y = self.apply_precond(r)
p = -y
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
def initialize_search(self):
""" Determines initial step length for line search
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
p = self.load('p_new')
f = loadtxt('f_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
# reset search history
self.search_history = [[0., f]]
self.step_count = 0
self.isdone = 0
self.isbest = 0
self.isbrak = 0
# determine initial step length
if self.iter == 1:
alpha = p_ratio * PAR.STEPINIT
elif self.restarted:
alpha = p_ratio * PAR.STEPINIT
elif PAR.SCHEME in ['LBFGS']:
alpha = 1.
else:
alpha = self.initial_step()
# optional ad hoc scaling
if PAR.STEPOVERSHOOT:
alpha *= PAR.STEPOVERSHOOT
# optional maximum step length safegaurd
if PAR.STEPTHRESH:
if alpha > p_ratio * PAR.STEPTHRESH and \
self.iter > 1:
alpha = p_ratio * PAR.STEPTHRESH
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha * p)
# upate log
self.stepwriter(steplen=0., funcval=f)
def initialize_search(self):
""" Determines initial step length for line search
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
p = self.load('p_new')
f = loadtxt('f_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m/norm_p)
# reset search history
self.search_history = [[0., f]]
self.step_count = 0
self.isdone = 0
self.isbest = 0
self.isbrak = 0
# determine initial step length
if self.iter == 1:
alpha = p_ratio*PAR.STEPINIT
elif self.restarted:
alpha = p_ratio*PAR.STEPINIT
elif PAR.SCHEME in ['LBFGS']:
alpha = 1.
else:
alpha = self.initial_step()
# optional ad hoc scaling
if PAR.STEPOVERSHOOT:
alpha *= PAR.STEPOVERSHOOT
# optional maximum step length safegaurd
if PAR.STEPTHRESH:
if alpha > p_ratio * PAR.STEPTHRESH and \
self.iter > 1:
alpha = p_ratio * PAR.STEPTHRESH
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha*p)
# upate log
self.stepwriter(steplen=0., funcval=f)
def update(self, ap):
unix.cd(self.path)
self.ilcg += 1
x = self.load('LCG/x')
r = self.load('LCG/r')
y = self.load('LCG/y')
p = self.load('LCG/p')
ry = loadtxt('LCG/ry')
pap = np.dot(p, ap)
if pap < 0:
print ' Stopping LCG [negative curvature]'
isdone = True
return isdone
alpha = ry / pap
x += alpha * p
r += alpha * ap
self.save('LCG/x', x)
self.save('LCG/r', r)
# check status
if self.check_status(ap) == 0:
isdone = True
elif self.ilcg >= self.maxiter:
isdone = True
else:
isdone = False
if not isdone:
y = self.apply_precond(r)
ry_old = ry
ry = np.dot(r, y)
beta = ry / ry_old
p = -y + beta * p
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
return isdone
def update(self, ap):
unix.cd(self.path)
self.ilcg += 1
x = self.load('LCG/x')
r = self.load('LCG/r')
y = self.load('LCG/y')
p = self.load('LCG/p')
ry = loadtxt('LCG/ry')
pap = np.dot(p, ap)
if pap < 0:
print ' Stopping LCG [negative curvature]'
isdone = True
return isdone
alpha = ry/pap
x += alpha*p
r += alpha*ap
self.save('LCG/x', x)
self.save('LCG/r', r)
# check status
if self.check_status(ap) == 0:
isdone = True
elif self.ilcg >= self.maxiter:
isdone = True
else:
isdone = False
if not isdone:
y = self.apply_precond(r)
ry_old = ry
ry = np.dot(r, y)
beta = ry/ry_old
p = -y + beta*p
self.save('LCG/y', y)
self.save('LCG/p', p)
savetxt('LCG/ry', np.dot(r, y))
return isdone
def compute_step(self):
""" Computes next trial step length
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m / norm_p)
x = self.step_lens()
f = self.func_vals()
# compute trial step length
if PAR.LINESEARCH == 'Fixed':
alpha = p_ratio * (self.step_count + 1) * PAR.STEPINIT
#elif PAR.LINESEARCH == 'Bracket' or \
# self.iter == 1 or self.restarted:
elif PAR.LINESEARCH == 'Bracket':
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = polyfit2(x, f)
elif any(f[1:] <= f[0]):
alpha = loadtxt('alpha') * PAR.STEPFACTOR**-1
else:
alpha = loadtxt('alpha') * PAR.STEPFACTOR
elif PAR.LINESEARCH == 'Backtrack':
# calculate slope along 1D profile
slope = s / self.dot(g, g)**0.5
if PAR.ADHOCFACTOR:
slope *= PAR.ADHOCFACTOR
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha * p)
def compute_step(self):
""" Computes next trial step length
"""
unix.cd(PATH.OPTIMIZE)
m = self.load('m_new')
g = self.load('g_new')
p = self.load('p_new')
s = loadtxt('s_new')
norm_m = max(abs(m))
norm_p = max(abs(p))
p_ratio = float(norm_m/norm_p)
x = self.step_lens()
f = self.func_vals()
# compute trial step length
if PAR.LINESEARCH == 'Fixed':
alpha = p_ratio*(self.step_count + 1)*PAR.STEPINIT
elif PAR.LINESEARCH == 'Bracket' or \
self.iter==1 or self.restarted:
if any(f[1:] < f[0]) and (f[-2] < f[-1]):
alpha = polyfit2(x, f)
elif any(f[1:] <= f[0]):
alpha = loadtxt('alpha')*PAR.STEPFACTOR**-1
else:
alpha = loadtxt('alpha')*PAR.STEPFACTOR
elif PAR.LINESEARCH == 'Backtrack':
# calculate slope along 1D profile
slope = s/self.dot(g,g)**0.5
if PAR.ADHOCFACTOR:
slope *= PAR.ADHOCFACTOR
alpha = backtrack2(f[0], slope, x[1], f[1], b1=0.1, b2=0.5)
# write trial model corresponding to chosen step length
savetxt('alpha', alpha)
self.save('m_try', m + alpha*p)
def compute_direction(self):
""" Computes model update direction from stored gradient
"""
unix.cd(PATH.OPTIMIZE)
g_new = self.load('g_new')
if PAR.SCHEME in ['GradientDescent', 'SteepestDescent']:
p_new, self.restarted = -g_new, False
elif PAR.SCHEME in ['NLCG']:
p_new, self.restarted = self.NLCG()
elif PAR.SCHEME in ['LBFGS']:
p_new, self.restarted = self.LBFGS()
self.save('p_new', p_new)
savetxt('s_new', self.dot(g_new, p_new))
return p_new
def restart(self):
""" Discards history of algorithm; prepares to start again from
gradient direction
"""
unix.cd(PATH.OPTIMIZE)
g = self.load('g_new')
self.save('p_new', -g)
savetxt('s_new', self.dot(g, g))
if PAR.SCHEME in ['NLCG']:
self.NLCG.restart()
elif PAR.SCHEME in ['LBFGS']:
self.LBFGS.restart()
self.restarted = 1
self.stepwriter.iter -= 1
self.stepwriter.newline()
def restart(self):
""" Discards history of algorithm; prepares to start again from
gradient direction
"""
unix.cd(PATH.OPTIMIZE)
g = self.load("g_new")
self.save("p_new", -g)
savetxt("s_new", self.dot(g, g))
if PAR.SCHEME in ["NLCG"]:
self.NLCG.restart()
elif PAR.SCHEME in ["LBFGS"]:
self.LBFGS.restart()
self.restarted = 1
self.stepwriter.iter -= 1
self.stepwriter.newline()
def compute_direction(self):
""" Computes model update direction from stored gradient
"""
unix.cd(PATH.OPTIMIZE)
g_new = self.load('g_new')
if PAR.SCHEME in ['GradientDescent', 'SteepestDescent']:
p_new, self.restarted = -g_new, False
elif PAR.SCHEME in ['NLCG']:
p_new, self.restarted = self.NLCG()
elif PAR.SCHEME in ['LBFGS']:
p_new, self.restarted = self.LBFGS()
self.save('p_new', p_new)
savetxt('s_new', self.dot(g_new, p_new))
return p_new
def compute_direction(self):
""" Computes model update direction from stored gradient
"""
unix.cd(PATH.OPTIMIZE)
g_new = self.load("g_new")
if PAR.SCHEME in ["SD"]:
p_new, self.restarted = -g_new, False
elif PAR.SCHEME in ["NLCG"]:
p_new, self.restarted = self.NLCG()
elif PAR.SCHEME in ["LBFGS"]:
p_new, self.restarted = self.LBFGS()
self.save("p_new", p_new)
savetxt("s_new", self.dot(g_new, p_new))
return p_new
def __call__(self):
""" Returns NLCG search direction
"""
self.iter += 1
savetxt(self.path+'/'+'NLCG/iter', self.iter)
unix.cd(self.path)
g_new = self.load('g_new')
if self.iter == 1:
return -g_new, 0
elif self.iter > self.maxiter:
print 'restarting NLCG... [periodic restart]'
self.restart()
return -g_new, 1
# compute search direction
g_old = self.load('g_old')
p_old = self.load('p_old')
if self.precond:
beta = pollak_ribere(g_new, g_old, self.precond)
p_new = -self.precond(g_new) + beta*p_old
else:
beta = pollak_ribere(g_new, g_old)
p_new = -g_new + beta*p_old
# check restart conditions
if check_conjugacy(g_new, g_old) > self.thresh:
print 'restarting NLCG... [loss of conjugacy]'
self.restart()
return -g_new, 1
elif check_descent(p_new, g_new) > 0.:
print 'restarting NLCG... [not a descent direction]'
self.restart()
return -g_new, 1
else:
return p_new, 0
def evaluate_function(cls):
m = loadnpy('m_try')
f = problem.func(m)
savetxt('f_try',f)
print f
def restart(self):
""" Restarts algorithm
"""
self.iter = 1
savetxt(self.path+'/'+'NLCG/iter', self.iter)
def evaluate_function(cls):
m = loadnpy('m_try')
f = problem.func(m)
savetxt('f_try', f)
print f
def evaluate_gradient(cls):
m = loadnpy('m_new')
f = problem.func(m)
g = problem.grad(m)
savetxt('f_new', f)
savenpy('g_new', g)
def evaluate_gradient(cls):
m = loadnpy('m_new')
f = problem.func(m)
g = problem.grad(m)
savetxt('f_new',f)
savenpy('g_new',g)
